Andreev Scattering in Semiconductor–Superconductor Junctions Containing a Finite Width Semiconductor Region Applied by Magnetic Fields

Abstract

We present numerical studies of conductance of quasi-particles (QPs) in junctions consisting of semiconductor (Sm) two-dimensional electronic gas (2DEG) and superconductor (S) containing a finite width 2DEG region (referred to magnetic barrier) applied by a magnetic field perpendicular to the 2DEG plane. Total conductance as a function of β=μ_N⁄hω_c (where μ_N is the chemical potential of semiconductor and ω_c=eB⁄cm^*_N is the cyclotron frequency) strongly depends on the normal or superconducting state of the superconductor. It demonstrates that the Andreev reflection (AR) plays a dominant role. The total conductance of G^(NBN) or G^(NBS) as a function of β for the NBN or NBS junction displays monotonically increasing behavior with different rising slopes. We observe the existence of a critical magnetic field for switching off the conductance. This critical field of G^(NBS) is a half of that of G^(NBN) in the matching case of the Fermi level and effective mass of QPs in materials forming the junctions. G^(NBS) is usually larger than G^(NBN) for a given magnetic field. The 3D plot of the conductance G^(NBN) and G^(NBS) as functions of β and the incident angle θ of the QPs displays a flat plateau over a finite domain region of [β,θ]. However, in the mismatching case of the Fermi energy and effective mass of QPs, G^(NBS) is lower than G^(NBN) because the AR of the holelike QPs now becomes incomplete and normal reflection (NR) of the electronlike QPs is considerably enhanced. The corresponding 3D plot of conductance against β and θ exhibits heavy spike oscillations around its occupied boundary. We present explicit analytic expressions of the conductance of QPs for this model junction on the basis of classical cyclotron orbit of the QPs in magnetic fields and the quantum mechanical calculation. The characteristics of conductance can be well interpreted by this phenomenological physical picture.